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The Humongous Book of Algebra Problems by W. Michael Kelley

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Chapter 2
RATIONAL NUMBERS
Chapter 1 introduced the concept of rational numbers, real numbers that
can be expressed as a fraction, a terminating decimal, or a repeating deci-
mal. Rational numbers are truly Gestalt, which is to say they are greater
than the sum of their parts. By nature they are merely quotients of integers,
but their complexity requires a unique set of concepts (such as the least
common denominator) and procedures (such as reducing to lowest terms
and transforming rational numbers from fractions to decimals and vice ver-
sa). Through the study of rational numbers, and the careful, often rigorous,
techniques that surround them, unique and otherwise obfuscated proper-
ties of integers are uncovered.
When you divide two integers, you get a fraction. The fancy name
for “fraction” is “rational number,” and that’s what you deal with in
this chapter. Fractions arent as hard to handle as most people think
you just need to know that when fractions are in the mix, you need
to follow specic rules. For instance, you can only add and subtract
fractions if they have the same denominator. Simple enough. However,
if fractions have DIFFERENT denominators, you CAN multiply and
divide them.
Spend some time getting familiar with fractions in this chapter. When
you nish, you’ll be able to change decimals into fractions; change
fractions into decimals; simplify fractions; identify a least common
denominator; and add, subtract, multiply, and divide fractions to your
heart’s content.
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